A bijection between permutation matrices and descending plane partitions without special parts, which respects the quadruplet of statistics considered by Behrend, Di Francesco and Zinn--Justin

TL;DR

This paper introduces a bijection linking permutation matrices and descending plane partitions without special parts, preserving key statistics, and utilizes inversion words and non-intersecting lattice paths.

Contribution

It provides a novel bijection that respects specific statistics, connecting permutation matrices with descending plane partitions in a new way.

Findings

Bijection preserves quadruple of statistics

Utilizes inversion words of permutations

Employs non-intersecting lattice paths representation

Abstract

We present a bijection between permutation matrices and descending plane partitions without special parts, which respects the quadruple of statistics considered by Behrend, Di Francesco and Zinn--Justin. This bijection involves the inversion words of permutations and the "usual" representation of descending plane partitions as families of non--intersec\-ting lattice paths.